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arXiv · 2407.05406

Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$

Qing-Ming Cheng·Yejuan Peng
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Abstract

In this paper, we study $n$-dimensional complete minimal hypersurfaces in a hyperbolic space $H^{n+1}(-1)$ of constant curvature $-1$. We prove that a $3$-dimensional complete minimal hypersurface with constant scalar curvature in $H^{4}(-1)$ satisfies $S\leq \frac{21}{29}$ by making use of the Generalized Maximum Principle, where $S$ denotes the squared norm of the second fundamental form of the hypersurface.

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Qing-Ming Cheng, Yejuan Peng. 2024-07-07. Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$. https://doi.org/10.2140/pjm.2025.338.251

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